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2 categories of experience rating
- no split plan: losses are not divided
- split plans: divided into primary & XS. Primary reflects frequency (most weight); XS represents severity
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2 categories of split plan
- single split: only one split into primary & excess
- multisplit: div into increments. Decr portion of each incr is primary
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Basic formula for no split plan
- M = [ZA + (1-Z)E] / E = 1 + Z [(A - E) / E], Z = E / (E + KE)
- 0 ≤ Z ≤ 1, d/dE(Z) ≥ 0, d/dE(Z/E) < 0
- if KE = k, M = (A + K) / (E + K)
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Split plans
- (+) better reflect diff types of WC clms (small, med, large w indemn)
- M = (1 / E) [ZpAp + (1-Zp)Ep + ZeAe + (1-Ze)Ee]
- M = 1 + Zp [(Ap - Ep) / E] + Ze [(Ae - Ee) / E]
- Zp = E / (E + KE), Ze = E / (E + JE)
- M = 1 + [(Ap - Ep)/(E + KE)] + [(Ae - Ee)/(E + JE)]
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Perryman's Formula
- goal: come up w a formula for M which does not include credibility constants
- M = [Ap + WAe + (1-W)Ee + (1-W)K] / [E + (1-W)K]
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Credibility from revised experience rating plan
- primary cr is greater for smaller risks
- excess cr is slightly greater for smaller risks
- primary cr is smaller for larger risks (capped at 91%) → no more self-rating
- XS cred much smaller for larger risk (cap 57%)
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Primary value formulae
- I = Increment or interval width
- 1940: Ap = Σ I(1-d)i + (1-d)N(A-NI); max(Ap) = I * (1/d)
- 1961: Ap = [A / (A + C)] (I + C)
- 1991: Ap capped at $5K
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